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Professor Howard Colquhoun tells the story of how an infinitely repeating pattern discovered in a plastic molecule relates to obscure 19th century maths – and Romanesco broccoli.

In 1874, Henry J. S. Smith, Professor of Geometry in the University of Oxford, had an interesting thought. “What would happen,” he wondered, “if you took a line, divided it into four, and then threw away the end quarter?”

Well, obviously, you would be left with a line three-quarters as long as the original.

But Smith’s next question was more subtle. “What would happen if you repeated this operation on the line that was left, and then continued to do this indefinitely?”

When Smith worked through the problem, it turned out that he had discovered the first ever example of a fractal, a mathematical structure that is made up of an infinite number of progressively smaller copies of itself.

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